207 
Æ | MDUÜMBRATIO® DEMONSTRATIONIS: THEOREMATIS ARITHME-- 
| TICI MAXIME- UNIVERSALIS. 
AUCTORE 
É F DEGEN. 
a 
Conventui exhibuit die 7. Octobris 1818. : 
——__— 
{. 1: Jamdudum nota suni Analysecos diophantéae cultoribus* 
séquentia: theoïemata :: 
I: Gp + q°): EE) — pEX à .< @s Ætgr}),- 
I GA + gg) fr + 98°) = pr + gqsŸ + fa PS + gr), 
ufide ,- Ÿ 05 = Vet g——a" ‘sequitur 
ITS (p° FD += as°) = (pr + aqs) + a (PS gr)’, 
néc” nôn° häéc : 
1e HQE RH 55 Go gt rt 59° 
= Pr + daERr HS) EP QpERs— 57) 
+ Pr Qs Rp + Sq)ÿ + Ps+ Qr — Rq — Sp}, 
qguod summo Æulero accéptum refertur’. et generalius hoc : 
V. @° — BQ° — CR? + BCR°) p° — Bg — Cr + BCs°) 
= Pp'+ BQg“+ CRr+ BCSs)— B(Pq + Qp + CRs + C8r) 
| —C(Pr— BQs + Rp + zu B$ q)° + BC@Ps — Qr + Rg + Spy° % 
…. quod ill. Zagrañge (V2. Mémoires de Berlin, annéè 1770. p. 133 
in fine), pracclaris: suis’ invéntis’ addidit,- quodque omnia praeceden-- 
dia: in se compléctitur.- Idem vero etiam' alio respectu est notatu 
| pen cum: ita efunciari possit : 
Si numerus formae: P° BBQ — CR BUS" per’ alium numé-” 
rm ejusdem formae, -puta p°—= bg —cr° +bcs" multiplicetur, 
prodibit: as ejusdem. formae, scil, F=V?— BX°— CY°+BCZ*,- 
sumendo” 
